Doug writes:
> While I understand linear computers, such as the ones which run MPE i/X, and
> neural networking type computers, albeit the concepts involve fuzzy thinking
> on my part, I do not have a clear concept of the Quantum Computer.
>
> How would it work?

Book:

   http://www.amazon.com/exec/obidos/ASIN/038794768X

Which explains the ideas and some of the applications, along with answers to
the "How would it work?" question, though you'll want to be comfortable with
at least some higher math if you actually want to feel like you really
understand it.  The book even includes code to simulate various Quantum
Computing systems, though you'll need a copy of Mathematica if you was to do
more than view the results.

The book is about three years old, but all the basic concepts are still
good.  There is also another book by the same authors (though I have't read
it) which is a year newer and looks like a less math-oriented book about
what Quantum Computing will mean, etc.:

   http://www.amazon.com/exec/obidos/ASIN/0387947698

> Is it true that once a problem is set up, a Quantum Computer can solve it
> instantly?

So far there are a few problems for which a quantum algorithm has been found
which is faster than any currently known classic algorithm.  These include
database searching, factoring integers, and one or two others.

There are also related fields like Quantum Cryptography, Teleportation,
etc., which are built out of the same components as a Quantum Computer, but
might not count in your definition of "Quantum Computing".

A Qunatum Computer can store more than one value in a "register" at the same
time.  In fact the number of values is conceptually unlimited.  So if you
want to find the factors of a big number, you can put all the pairs of
possible factors into two quantum registers, then in a single operation you
can multiply all of the values in the first register by the corresponding
values in the second register, leaving all the results in a third register.
If any of the pairs of numbers were factors of the original number, then
that original number will be among the values in the result register.

The trick is to be able to extract the result you're interested in from the
result register, since reading it will only give you one result and all of
them are equally likely to be read out to you.  It turns out that for
factoring there are some really obscure results from number theory that give
you a way to use a Quantum Computer to factor integers, but this result does
not generalize Quantum Computers to be able to solve arbitrary problems
arbitrarily fast.

> Perhaps some on this forum would know.

Bruce and perhaps Wirt probably know more about it than I do.

G.